How can a prime element in a Ring be proven as irreducible?

NoodleDurh
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How does one show that a prime element in a Ring is irreducible and how does one show that ##|| x || = 1## iff x is a unit.

okay from my knowledge I know that units are invertible elements, so how does the norm of x make it 1... maybe I am not too sure about this
 
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For your first question, try doing a proof by contradiction. Let p be a prime element, and suppose it is reducible. What can you do with that?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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